The balancing of chemical equations can be done systematically. Some chemists still prefer trial and error, which means that you start with one atom and then go back and forth until you obtain a consistent solution. However, I strongly recommend the algebraic method, which is based on the principle of conservation of mass for each atomic species. You apply unknown coefficientsa, b, c, etc. to the reactants and x, y, z, etc. to the products. Then you set up "atomic equations", which multiple each coefficient by the number of atoms in the molecules that it stands for. Then you choose one initial value. Normally, this initial value will automatically determine all of the other values. You might ask: why do I need to choose an initial value? The answer that stoichiometry gives you a ratio between each reactant and product molecule, but the absolute values can be scaled. For example, the reactions
2 H2 + O2 = 2 H2O
H2 + 1/2 O2 = H2O
are really the same. THe ratios between the reacting species are the same. If we multiply each coefficient in the bottom reaction by 2 we obtain the top reaction. Let's take a look at how this works in practice.
